Methods for providing a selection of a recommended golf ball

ABSTRACT

Methods for evaluating and providing selections of recommended golf balls, golf ball constructions, and configurations of golf ball construction components are provided. Such methods may involve obtaining or measuring spin measurements against a plurality of golf clubs for each of a plurality of golf balls. A linear relationship may be used to determine a spin slope for each golf ball on the basis of the set of spin measurements associated with that golf ball. In turn, a selection of a recommended golf ball, golf ball construction, or configuration of a ball construction component may be made based upon which golf ball has the larger spin slope.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority under 35 U.S.C. §119(e) to U.S.Provisional Patent Application No. 61/526,660, entitled “Methods ForSelecting Golf Balls,” and filed on Aug. 23, 2011, which application ishereby incorporated by reference.

BACKGROUND

The game of golf first centered around striking balls of worked woodaround a course. In time, the wooden balls were surpassed in performanceby leather-cover, feather-stuffed balls (“featheries”), which were inturn surpassed and replaced by gum-based gutta-percha balls (“gutties”).A century and more ago, balls with thread-wound rubber cores and dimpledcovers came to dominate the sport. More modernly, advances in variouscomponents of golf ball construction—such as the number of pieces orlayers, the materials incorporated therein, and the configuration andnumber of dimples—have led to improved performance characteristics. Suchadvances have addressed the constant question: “What would make a golfball better?”

One challenge involved in making a better golf ball is to improve a golfball's performance characteristics all the way from the tee to the hole.For example, various components of golf ball construction might bemodified to make a ball that is less prone to spinning. The reduced spinmay improve a golfer's long game (i.e., shots taken relatively far froma hole) by increasing distances achieved when striking the ball with adriver, such as at the tee. However, a ball that is less prone tospinning may at the same time worsen the golfer's short game (i.e.,shots taken relatively near a hole) by hindering a ball's ability toquickly come rest after being struck with a wedge closer to the green.Conversely, modifying various components of golf ball construction tomake a ball that is more prone to spinning might improve a golfer'sshort game by allowing a ball to quickly come to rest when struck with awedge, but might at the same time hinder the golfer's long game byshortening the trajectory of the ball due to the increased spin on theball.

There is a need to modify various golf ball construction components insuch a way as to improve performance seen not just off the tee, and notjust near or on the green, but “across the bag” or at all distances fromthe hole, i.e., to improve both the long games and the short games ofgolfers. Accordingly, there is a need to evaluate and provide aselection among various golf balls, or among various golf ballconstructions, to assist in the specification and manufacture of golfballs that will improve a golfer's performance across the entire rangeof golf clubs. In a similar vein, there is a need to evaluate theperformance characteristics inherent in a particular golfer's swings inorder to assist in providing a selection of a recommended golf ball thatmay improve the golfer's performance across the entire range of golfclubs.

SUMMARY

In one aspect, the invention includes a method for providing a selectionof a recommended golf ball. In one step, the method includes obtaining(a) a first set of measurements for a first golf ball, including atleast one ball spin measurement for each of a plurality of golf clubshaving different club lofts, and (b) a second set of measurements for asecond golf ball, including at least one ball spin measurement for eachof the plurality of golf clubs. In another step, the method includesdetermining (a) a first spin slope based upon the first set ofmeasurements, and (b) a second spin slope based upon the second set ofmeasurements. In another step, the method includes providing a selectionof a recommended golf ball between the first golf ball and the secondgolf ball. The recommended golf ball is the first golf ball if the firstspin slope is larger than the second spin slope, and the recommendedgolf ball is the second golf ball if the first spin slope is not largerthan the second spin slope.

In another aspect, the invention includes a method for providing aselection of a recommended golf ball construction. In one step, themethod includes obtaining (a) a first set of measurements using a firstgolf ball having a first ball construction, including at least one ballspin measurement for each of a first golf club having a first club loftand a second golf club having a second club loft, and (b) a second setof measurements using a second golf ball having a second ballconstruction, including at least one ball spin measurement for each ofthe first golf club and the second golf club. In another step, themethod includes determining (a) a first linear relationship among thefirst set of measurements, and (b) a second linear relationship amongthe second set of measurements. In another step, the method includesproviding a selection of a recommended golf ball construction betweenthe first ball construction and the second ball construction. Therecommended golf ball construction is the first ball construction if aslope of the first linear relationship is larger than a slope of thesecond linear relationship, and the recommended golf ball constructionis the second ball construction if the slope of the first linearrelationship is not larger than the slope of the second linearrelationship, and wherein the first ball construction is different fromthe second ball construction.

In another aspect, the invention includes a method for providing aselection of a recommended configuration of a golf ball constructioncomponent. In one step, the method includes measuring (a) a first ballspin upon striking a first golf ball with a first golf club having afirst club loft, (b) a second ball spin upon striking the first golfball with a second golf club having a second club loft, (c) a third ballspin upon striking a second golf ball with the first golf club, and (d)a fourth ball spin upon striking the second golf ball with the secondgolf club. In another step, the method includes determining (a) a firstspin slope for the first golf ball, to include the ratio of (1) adifference between the second ball spin and the first ball spin to (2) adifference between the second club loft and the first club loft, and (b)a second spin slope for the second golf ball, to include the ratio of(1) a difference between the fourth ball spin and the third ball spin to(2) the difference between the second club loft and the first club loft.In another step, the method includes providing a selection of arecommended configuration of a golf ball construction component on thebasis of at least the first spin slope, the second spin slope, and aspin slope criteria. The configuration of the ball constructioncomponent of the second golf ball is different from the configuration ofthe ball construction component of the first golf ball.

In another aspect, the invention includes a golf ball performancecharacterization for use in a golf ball fitting system. The golf ballperformance characterization comprises a linear relationship among atleast a first ball spin measurement, a second ball spin measurement, anda third ball spin measurement. The first ball spin measurement isobtained upon striking a golf ball with a first golf club having a firstclub loft. The second ball spin measurement being obtained upon strikingthe golf ball with a second golf club having a second club loft greaterthan the first club loft. The third ball spin measurement being obtainedupon striking the golf ball with a third golf club having a third clubloft greater than the second club loft.

In another aspect, the invention includes a method for providing aselection of a recommended golf ball. In one step, the method includesobtaining (a) a first set of ball spin measurements from a player makingstrikes with a first plurality of striking objects having differentlofts, and (b) a second set of ball spin measurements from referencestrikes made with a second plurality of striking objects havingdifferent lofts. In another step, the method includes determining (a) afirst linear relationship among the first set of ball spin measurements,and (b) a second linear relationship among the second set of ball spinmeasurements. In another step, the method includes providing a selectionof a recommended golf ball between a first golf ball and a second golfball on the basis of at least the first linear relationship, the secondlinear relationship, and a spin slope criteria. The configuration of aball construction component of the second golf ball is different fromthe configuration of the ball construction component of the first golfball.

In another aspect, the invention includes a method for providing aselection of a recommended golf ball. In one step, the method includesobtaining (a) a first ball spin measurement upon striking a first golfball with a first golf club having a first club loft, (b) a second ballspin measurement upon striking the first golf ball with a second golfclub having a second club loft, (c) a third ball spin measurementassociated with striking a second golf ball with a third golf clubhaving a third club loft, and (d) a fourth ball spin measurementassociated with striking the second golf ball with a fourth golf clubhaving a fourth club loft. In another step, the method includesdetermining (a) a first spin slope for the first golf ball, the firstspin slope including the ratio of (1) a difference between the secondball spin measurement and the first ball spin measurement to (2) adifference between the second club loft and the first club loft, and (b)a second spin slope for the second golf ball, the second spin slopeincluding the ratio of (1) a difference between the fourth ball spinmeasurement and the third ball spin measurement to (2) the differencebetween the fourth club loft and the third club loft. In another step,the method includes providing a selection of a recommended golf ball onthe basis of at least the first spin slope, the second spin slope, and aspin slope criteria. The configuration of a ball construction componentof the second golf ball is different from the configuration of the ballconstruction component of the first golf ball.

Other systems, methods, features, and advantages of the invention willbe, or will become, apparent to one of ordinary skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description and this summary, bewithin the scope of the invention, and be protected by the followingclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale; instead, emphasis is placed upon illustrating theprinciples of the invention. Moreover, in the figures, like referencenumerals designate corresponding parts throughout the different views.

FIG. 1 depicts a golfer using a first embodiment of a golf ball alongwith a first embodiment of a golf club;

FIG. 2 depicts the golfer using the first embodiment of the golf ballalong with a second embodiment of the golf club;

FIG. 3 depicts the golfer using a second embodiment of the golf ballalong with the first embodiment of the golf club;

FIG. 4 depicts the golfer using the second embodiment of the golf ballalong with the second embodiment of the golf club;

FIG. 5 depicts the first embodiment of the golf club;

FIG. 6 depicts the second embodiment of the golf club;

FIGS. 7-9 depict alternate embodiments of the golf ball having differentconfigurations of layers;

FIGS. 10-12 depict alternate embodiments of the golf ball havingdifferent configurations of dimples;

FIGS. 13-15 depict alternate embodiments of the golf ball havingdifferent configurations of cover layer thickness;

FIG. 16 depicts a set of data points corresponding with the firstembodiment of the golf ball, and a slope therebetween, in an x/ycoordinate system;

FIGS. 17-19 depict alternate embodiments of the x/y coordinate system;

FIG. 20 depicts sets of data points associated with the first embodimentof the golf ball and the second embodiment of the golf ball, and theslopes therebetween;

FIGS. 21-24 depict sets of data points associated with alternateembodiments of the golf ball;

FIG. 25 depicts a set of data points associated with another alternateembodiment of the golf ball; and

FIGS. 26-27 depict further alternate sets of data points associated withfurther alternate embodiments of the golf ball.

DETAILED DESCRIPTION

Methods for providing a selection of a recommended golf ball aredescribed below. Also described are methods for providing a selection ofa recommended golf ball construction, as well as methods for providing aselection of a recommended configuration of a golf ball constructioncomponent.

FIG. 1 depicts a golfer 1000 playing a game of golf on a fairway 1060 ofa golf course 1050. Golfer 1000, still far from the hole, has made agolf shot by swinging at and striking a first golf ball 1100 with afirst golf club 1200. Since golfer 1000 is still playing on an earlyportion of fairway 1060, first golf club 1200 may be a driver, such as awood, or another club designed primarily to assist golfer 1000 inachieving maximum distance as a result of the swing. As depicted in FIG.5, first golf club 1200 has a first club loft 1202 representing theangle of the club's face relative to a vertical line (i.e., a lineparallel to the club shaft). First club loft 1202 of first golf club1200 is in the low range of golf club lofts, which helps a golfermaximize the distance achieved on striking a golf ball.

Returning to FIG. 1, in the course of swinging, golfer 1000 has aimed ata first target spot 1210. The strike resulting from the swing has sentfirst golf ball 1100 along a first trajectory 1220 to hit fairway 1060at a first contact spot 1230 near first target spot 1210. After hittingfirst contact spot 1230, first golf ball 1100 may bounce or roll somedistance from first contact spot 1230 and come to rest at first stoppingspot 1240.

Proceeding, FIG. 2 depicts golfer 1000 at a time when play has advancedclose to a hole 1080. Golfer 1000, now on a green 1070, has made anothergolf shot by swinging at and striking first golf ball 1100 with a secondgolf club 1300. Since golfer 1000 is playing on green 1070 and close tohole 1080, second golf club 1300 may be a wedge, such as a pitchingwedge, or another club designed primarily to assist golfer 1000 inachieving a relatively shorter, controlled distance as a result of theswing. As depicted in FIG. 6, second golf club 1300 has a second clubloft 1302 representing the angle of the club's face relative to avertical line (i.e., a line parallel to the club shaft). Second clubloft 1302 is in the high range of golf club lofts, which helps a golfermore precisely control the final position of a golf ball achieved upon astrike.

Returning to FIG. 2, in the course of swinging, golfer 1000 has aimed ata second target spot 1310 near hole 1080. The strike resulting from theswing has sent first golf ball 1100 along a second trajectory 1320 tohit green 1070 at a second contact spot 1330 near second target spot1310. After hitting second contact spot 1330, first golf ball 1100 maybounce or roll some distance from second contact spot 1330 and come torest at second stopping spot 1340.

Generally speaking, golf shots may be affected by various golf shotparameters. Some golf shot parameters may be swing parameters, and maybe influenced by the mechanics or specifics of a golfer's swing. Othergolf shot parameters may be launch condition parameters, and may beinfluenced by both the golfer's swing mechanics and by the constructionof a golf ball. Further golf shot parameters may be ball flightparameters, and may be influenced both by the construction of the golfball and by environmental conditions. Various golf shot parameters mayalso be influenced by the construction of the golf club used in makingthe golf shot.

Some swing parameters may include a swing speed, a club path, and anattack angle. The swing speed may be a club head speed. The club pathmay include a position of the club head, a face angle, or a loft, whichmay be measured statically at a particular time (such as the moment ofimpact or contact between ball and club) and with respect to a static orreference position (such as measuring loft and lie angles with respectto a golf club shaft in the vertical plane, for example). The club pathmay also include a path or direction of the club head, as representedfor example by a multi-dimensional vector. The attack angle may be amulti-dimensional angle in a plane defined by a vertical referencedirection and an intended or target direction.

Launch condition parameters may include a launch angle, a ball speed orinitial velocity, a ball spin, or an initial direction. The ball spinmay be either a ball back-spin (i.e., a spin about a horizontal axis) ora ball side-spin (i.e., an angle of backspin relative to a horizontalplane). The initial direction may be an angle relative to an intendedtarget direction, such as an offline angle. Furthermore, an initialangle may be a launch condition parameter combining the launch angle andthe offline angle. Launch condition parameters may also include acousticparameters such as the quality of sound made when a ball is struck.

Ball flight parameters may include parameters related to ballconstruction, such as dimple count, dimple configuration, and moment ofinertia. Ball flight parameters may also include parameters related toenvironmental conditions, such as wind characteristics (i.e. wind speedand direction), elevation, relative humidity, and weather conditions(i.e. rain, sleet, hail, or snow). Other golf shot parameters mayinclude carry or flight distance, roll distance, and total distance.

Returning to FIGS. 1 and 2, first trajectory 1220 and second trajectory1320 may be characterized by golf shot parameters such as initial angle,ball back-spin, ball side-spin, and initial velocity. Each of theseparameters may be affected by a golfer's choice of golf club. Forexample, ball back-spin may be relatively low for balls struck with aclub like first golf club 1200. In turn, a relatively low ball back-spinmay help a golfer maximize the distance achieved on a strike byproviding for a relatively straighter trajectory. Alternatively, ballback-spin may be relatively high for balls struck with a club likesecond golf club 1300. In turn, a relatively high ball back-spin mayhelp a golfer more precisely control the final position of a golf ballachieved upon a strike by counteracting the ball's tendency to bounce orroll away from a contact spot.

At the same time, the construction of a golf ball may affect the golfball's trajectory upon being hit, such as shape of the trajectory, orthe distance over which the trajectory extends. The construction of agolf ball may also affect the manner in which the golf ball bounces orrolls between a contact spot where it hits the ground and a stoppingspot where it comes to rest. Accordingly, the construction of first golfball 1100 may impact first trajectory 1220, the manner in which firstgolf ball 1100 bounces or rolls between first contact spot 1230 andfirst stopping spot 1240, or both. Similarly, the construction of firstgolf ball 1100 may also impact second trajectory 1320, the manner inwhich first golf ball 1100 bounces or rolls between second contact spot1330 and second stopping spot 1340, or both.

In general, the construction of a particular golf ball includes a numberof components. Pertinent ball construction components may include, forexample: the number of pieces or layers within the golf ball; the golfball's cover material; the hardness of the golf ball's cover material;materials used for one or more core portions, such as an inner core, anouter core, or both, as well as intermediately layers, such as one ormore mantle layers, for example; the number of dimples in the golfball's cover; and the thickness of the golf ball's cover. Other ballconstruction components may include, for example: the shape, pattern, orother configuration of the dimples in the golf ball's cover; aestheticconsiderations such as color or indicia; and other aspects ofconstruction affecting the physical response of the golf ball toexternal stimulus.

Each piece or layer of the construction used for cover portions of agolf ball as well as for core portions of a golf ball, may have physicalcharacteristics, such as a thickness, and may be formed from any of avariety of materials. Each material used to form a piece or layer of theconstruction may in turn have physical characteristics such as density,and hardness, for example. Moreover, a physical characteristic of thematerial within a particular piece or layer of the construction may varywithin that piece or layer. The physical characteristic of the materialof the piece or layer may not be constant throughout the piece or layer,but may be vary as a function of, for example, a distance at each pointwithin the material from the center of the golf ball. That is, thephysical characteristic may be a gradient within the material.

Generally, for any arrangement of layers not specifically mentionedherein, any layer may be made of any material suitable for the purpose.Suitable known materials for use in a golf ball include thermosetmaterials, such as rubber, styrene butadiene, polybutadiene, isoprene,polyisoprene, certain types of polyurethanes, and trans-isoprene. Knownmaterials also include thermoplastics, such as ionomer resins,polyamides or polyesters, and thermoplastic polyurethane elastomers.Suitable materials also include polyurea compositions, as well as othermaterials.

For example, a cover layer should be tough and resistant to scuffingwhile being soft enough for a golf club to impart spin easily to theball. Thus, thermoplastic polyurethane (TPU) and thermoset polyurethaneare suitable for use in cover layers, as are known highly neutralizedpolymers and other ionomers. Thermoplastic polyurethane that is nototherwise scuff resistant can be treated to harden the surface, such asby a surface treatment or by other treatments before, during, and/orafter molding the layer. Suitable ionomers include members of theSurlyn® family of ionomeric polymers produced by E. I. DuPont de Nemoursand Company and members of the Iotek® family of products produced byExxonMobil Chemical Corporation. Additionally, other traditionalmaterials for covers may also be used, such as balata.

Each golf ball construction component specifies something about thenature of one or more portions of a golf ball. Accordingly, with respectto FIGS. 1 and 2, when golfer 1000 makes a golf shot by swinging at andstriking a golf ball, one or more components of the golf ball'sconstruction may impact the trajectory of the golf ball, or the mannerin which the golf ball bounces or rolls between a contact spot where ithits the ground and a stopping spot where it comes to rest.

One or more ball construction components may therefore impact one ormore golf shot parameters such as the initial angle, the ball back-spin,the ball side-spin, and the initial velocity. Moreover, a particularconfiguration of a golf ball construction component may affect the golfball's trajectory in one way when struck by a club having a low loftangle, and may affect the golf ball's trajectory in another differentway when struck by a club having a high loft angle.

FIG. 3 depicts golfer 1000 playing golf on fairway 1060 of golf course1050. As with FIG. 1, golfer 1000, being far from the hole, has made agolf shot with first golf club 1200. However, in FIG. 3, golfer 1000 hasswung at a second golf ball 2100, which has a construction differentfrom the construction of first golf ball 1100.

More particularly, the configuration of one or more underlying ballconstruction components in second golf ball 2100 is different from theconfiguration of the same underlying ball construction components infirst golf ball 1100. As a result, second golf ball 2100 may performdifferently than first golf ball 1100 would perform given substantiallythe same swing. Differences in the configurations of the underlying ballconstruction components between second golf ball 2100 and first golfball 2200 may impact such golf shot parameters as initial angle, ballback-spin, ball side-spin, and initial velocity.

Golfer 1000 has swung golf club 1200 in substantially the same way inFIG. 3 as in FIG. 1, and has aimed at first target spot 1210. However,due to differences in ball construction components between second golfball 2100 and first golf ball 1100, first trajectory 1220 for secondgolf ball 2100 extends over a greater distance. As a result, firstcontact spot 1230 and first stopping spot 1240 upon using second golfball 2100 are farther away from golfer 1000 than first contact spot 1230and first stopping point 1240 upon using first golf ball 1100. Sincegolfer 1000 has swung first golf club 1200 in substantially the same wayin FIG. 3 as in FIG. 1, these differences are due to differences in theunderlying ball construction components between second golf ball 2100and first golf ball 1100, which have impacted golf shot parameters suchas initial angle, ball back-spin, ball side-spin, and initial velocity.

For example, differences in one or more ball construction components ofsecond golf ball 2100 may result in the ball back-spin of second golfball 2100 resulting from a swing of first golf club 1200 being reducedrelative to the ball back-spin of first golf ball 1100 resulting fromsubstantially the same swing of first golf club 1200. This reduced ballback-spin of second golf ball 2100 due to the difference in ballconstruction components may help a golfer maximize the distance achievedon striking second golf ball 2100 with first golf club 1200.

Turning to FIG. 4, golfer 1000 is playing golf on fairway 1060 of golfcourse 1050, on green 1070. As with FIG. 2, golfer 1000, being on green1070 and close to hole 1080, has made a golf shot with second golf club1300. However, in FIG. 4, golfer 1000 has swung at second golf ball2100.

Golfer 1000 has swung second golf club 1300 in substantially the samewas in FIG. 4 as in FIG. 2, and has aimed at second target spot 1310while swinging, and has achieved substantially the same secondtrajectory 1320 upon striking second golf ball 2100. However, due todifferences in ball construction components between second golf ball2100 and first golf ball 1100, the manner in which second golf ball 2100has travelled between second contact spot 1330 and second stopping spot1340 is different than the manner in which first golf ball 1100travelled between second contact spot 1330 and second stopping spot1340. Since golfer 1000 has swung second golf club 1300 in substantiallythe same way in FIG. 4 as in FIG. 2, these differences are due todifferences in the underlying ball construction components betweensecond golf ball 2100 and first golf ball 1100, which have impacted golfshot parameters such as initial angle, ball back-spin, ball side-spin,and initial velocity.

For example, differences in one or more ball construction components ofsecond golf ball 2100 may result in the ball back-spin of second golfball 2100 resulting from a swing of second golf club 1300 beingincreased relative to the ball back-spin of first golf ball 1100resulting from substantially the same swing of second golf club 1300.The increased ball back-spin of second golf ball 2100 due to thedifference in ball construction components may help a golfer moreprecisely control the final position of second golf ball achieved uponstriking second golf ball 2100 with second golf club 1300.

Moreover, the different configuration of ball construction components ofsecond golf ball 2100 that may reduce ball back-spin when struck withfirst golf club 1200 may also advantageously increase ball back-spinwhen struck with second golf club 1300. In other words, a difference inconfiguration between the ball construction components of two golf ballsmay improve results obtained from swings with more than one type of golfclub. A change in configuration of any of a number of ball constructioncomponents of first golf ball 1100 may accordingly result in improvedperformance on the golf course with more than one type of golf club.

Any of a number of ball construction components of first golf ball 1100may be modified to alter the performance of first golf ball 1100 whenstruck by golf clubs 1200 and 1300. As depicted in FIG. 7, first golfball 1100 may be configured to have a three-piece or three-layerconstruction including a first layer 1151, a second layer 1152, and athird layer 1153. However, the configuration of first golf ball 1100 maybe modified such that golf ball 1100 has more pieces or layers, or fewerpieces or layers. For example, as depicted in FIG. 8, first golf ball1100 may be configured to have a four-piece or four-layer constructionincluding first layer 1151, second layer 1152, third layer 1153, and afourth layer 1154. Alternatively, as depicted in FIG. 9, first golf ball1100 may be configured to have a two-piece or two-layer constructionincluding only first layer 1151 and second layer 1152.

Alternatively, FIG. 10 depicts first golf ball 1100 as having aconfiguration in which first layer 1151, a cover layer, has a firstnumber of dimples 1155. The configuration of first golf ball 1100 may bemodified, though, such that golf ball 1100 has more dimples or fewerdimples. As in the example depicted in FIG. 11, first golf ball 1100 maybe configured to have a second number of dimples 1155 greater than thefirst number of dimples 1155 of FIG. 10. In contrast, as in the exampledepicted in FIG. 12, first golf ball 1100 may be configured to have athird number of dimples 1155 less than the first number of dimples 1155.

Meanwhile, FIG. 13 depicts golf ball 1100 as having a configuration inwhich first layer 1151, a cover layer, has a first thickness. In otherconfigurations, first layer 1151 may be modified to have otherthicknesses. In one example depicted in FIG. 14, first layer 1151 hasbeen configured to have a second thickness greater than the firstthickness. In another example depicted in FIG. 15, first layer 1151 hasbeen configured to have a third thickness less than the first thickness.

Other ball construction components of golf ball 1100 may have alternateconfigurations as well. For example, the configuration of material ormaterials incorporated in any of layers 1151-1154 of golf ball 1100depicted in FIGS. 7-9 may be altered. Moreover, a hardness of a materialor materials incorporated in any of layers 1151-1154 of golf ball 1100may also be altered.

Accordingly, the configuration of various ball construction componentsof first golf ball 1100 may be modified, as indicated above, to arriveat the ball construction components of second golf ball 1200.Subsequently, the effect on performance due to the modifications of theconfiguration of first golf ball 1100 may be evaluated. In suchevaluations, a first data point 151 may be gathered by striking firstgolf ball 1100 with first golf club 1200 and a second data point may begathered by striking first golf ball 1100 with second golf club 1300.Similarly, a third data point 153 may be gathered by striking secondgolf ball 2100 with first golf club 1200 and a fourth data point may begathered by striking second golf ball 2100 with second golf club 1300.

As depicted in FIGS. 20-24, each of data points 151-154 may have atleast two values and may be graphically represented in a two-valuecoordinate system, such as x/y coordinate system 100 having an x-axis110 and a y-axis 120. A first value of data points 151-154 may representthe club loft associated each particular strike, while a second value ofdata points 151-154 may represent the golf ball back-spin associatedwith each particular strike. In the context of x/y coordinate system100, the first values of data points 151-154 may establish x-coordinatesof data points 151-154 within x/y coordinate system 100, and the secondvalues of data points 151-154 may establish y-coordinates of data points151-154 within x/y coordinate system 100.

Therefore, as described above and as depicted in FIGS. 20-24, the firstvalues of data points 151 and 152 would represent, respectively, (a)first club loft 1202 and (b) second club loft 1302, while the secondvalues of data points 151 and 152 would represent, respectively, (a) aball back-spin value obtained from striking first golf ball 1100 withfirst golf club 1200, and (b) a ball back-spin value obtained fromstriking first golf ball 1100 with second golf club 1300. Similarly, thefirst values of data points 153 and 154 would represent, respectively,(a) first club loft 1202 and (b) second club loft 1302, while the secondvalues of data points 153 and 154 would represent, respectively, (a) aball back-spin value obtained from striking second golf ball 2100 withfirst golf club 1200, and (b) a ball back-spin value obtained fromstriking second golf ball 2100 with second golf club 1300.

Moreover, a first line may relate data points 151 and 152 to each other,and a second line may relate data points 153 and 154 to each other. Eachof the first line and the second line may have a “spin slope” that isthe ratio of a difference between y-values of a set of two points alongthe line to a difference between x-values of the same set of two points(i.e., a ratio of “rise” to “run” along the line). For example, a firstspin slope 201 of the line relating first data point 151 to second datapoint may be the ratio of (1) the difference between the y-value ofsecond data point 152 and the y-value of first data point 151 to (2) thedifference between the x-value of second data point 152 and the x-valueof first data point 151. First spin slope 201 may accordingly be a spinslope associated with first golf ball 1100. Similarly, a second spinslope 202 may be a spin slope associated with second golf ball 2100.

The x-values and y-values associated with each data point may be valuesas objectively measured, or they may be reduced or simplifiedrepresentations of objectively-measured values. For example, as depictedin FIG. 16, the x-values are club lofts, measured in degrees, while they-values are ball back-spins, measured in RPM (revolutions per minute).

In contrast, as depicted in FIG. 17, the x-values are reduced orsimplified representations of objectively-measured values. Inparticular, the x-axis has been normalized such that data point 151obtained by striking a golf ball with first golf club 1100 has anx-value represented as “D,” while data point 152 obtained by striking agolf ball with second golf club 1200 has an x-value represented as “W.”In such reduced or simplified depictions, the difference between thex-values of data points 151 and 152 may be arbitrarily set to “1,” andthe spin slope 201 of the line relating data points 151 and 152 reducesto a difference between the y-values (i.e., the ball back-spin) of datapoints 151 and 152. That is, spin slope 201 reduces to a normalizeddifference between the ball back-spin values of data point 151 and 152.

Alternatively, as depicted in FIG. 18, the x-values of data points 151and 152 are objectively-measured values, while the y-values of datapoints 151 and 152 are normalized relative to the lowest y-value (i.e.,the y-value of data point 151) and are represented along y-axis 120 asmultiples of a number labeled S_(D). In turn, S_(D) may be the ballback-spin associated with first golf club 1200, which may be a driver.In such reduced or simplified depictions, the y-value of data point 151is reduced to 1 S_(D), while the y-value of data point 152 is reduced toapproximately 2.25 S_(D). That is, spin slope 201 becomes the ratio of adifference in the normalized multiple of S_(D) units between data points151 and 152 to the difference between the x-values (i.e., club lofts) ofdata points 151 and 152.

As a further alternative, both the x-values and the y-values may bereduced or simplified. For example, as depicted in FIG. 19, thereduction or simplification of x-values of FIG. 17 is combined with thereduction or simplification of y-values of FIG. 18, such that spin slope201 reduces to of a normalized multiple of S_(D) units between datapoints 151 and 152.

The differing configurations of ball construction components betweenfirst golf ball 1100 and second golf ball 1300 may result in differingresponses, such as differing ball back-spin measurements, upon strikesmade with first golf club 1200, second golf club 1300, or both. Invarious configurations of ball construction components, the ballback-spin of second golf ball 2100 might be greater than or less thanthe ball back-spin of first golf ball 1100 when struck by either firstgolf club 1200 or second golf club 1300.

For example, as depicted in FIG. 20, ball back-spin values for datapoints 153 and 154 corresponding with second golf ball 1200 are greaterthan ball back-spin values for data points 151 and 152 correspondingwith first golf ball 1100. That is, second golf ball 2100 is measured ashaving a greater ball back-spin than first golf ball 1200 when struckeither with first golf club 1200 or with second golf club 1300. Incontrast, as depicted in FIG. 21, second golf ball 2100 is measured ashaving less ball back-spin than first golf ball 1100 when struck eitherwith first golf club 1200 or with second golf club 1300. Accordingly, asdepicted in FIGS. 20 and 21, the second spin slope 202 and the firstspin slope 201 are substantially similar.

In other configurations, the ball back-spin of second golf ball 2100might differ from the ball back-spin of first golf ball 1100 when struckby either first golf club 1200 or second golf club 1300, but not both.For example, as depicted in FIG. 22, a ball back-spin value for datapoint 153 is less than a ball back-spin value for data point 151, whileball back-spin values for data points 152 and 154 are substantiallysimilar.

Alternatively, as depicted in FIG. 23, a ball back-spin value for datapoint 154 is greater than a ball back-spin value for data point 152,while ball back-spin values for data points 151 and 153 aresubstantially similar. Accordingly, as depicted in FIGS. 22 and 23, thesecond spin slope 202 is greater than first spin slope 201. Ballconfigurations producing ball back-spin values that change for eitherfirst golf club 1200 or second golf club 1300, but not both (i.e., thatdo not change ball back-spin values across the bag), may be useful forgolfers who need more spin in some areas of their game than in others.

In still further configurations, the ball back-spin of second golf ball2100 might be less than the ball back-spin of first golf ball 1100 whenstruck by first golf club 1200, but might be greater than the ballback-spin of first golf ball 1100 when struck by second golf club 1300.For example, as depicted in FIG. 24, a ball back-spin value for datapoint 153 is less than a ball back-spin value for data point 151, and aball back-spin value for data point 154 is greater than a ball back-spinvalue for data point 152. Accordingly, the second spin slope 202 isgreater that the first spin slope 201.

Data points such as those described above may include compositemeasurements. For example, y-values (i.e., ball back-spin) values may bestatistically extracted from a desired set of measurements, such asrepeated measurements of ball back-spin taken under substantiallysimilar conditions. Values that may be statistically extracted from suchsets of measurements may include average or mean values, includingarithmetic means or geometric means, median values, or standarddeviations. As depicted in FIG. 25, for example, data points 151 and 152both include composite measurements representing the average value ofset of measurements having a substantially normal distribution.

Additionally, while spin slope may be determined from data pointsassociated with two distinct values of club loft, as discussed above,linear relationships between data points associated with more than twodistinct values of club loft. Once such a linear relationship has beendetermined, a slope may be determined on the basis of that linearrelationship. For example, as depicted in FIG. 26, four data points 151,152, 153, and 153 corresponding with ball back-spin measurements havebeen obtained using four golf clubs having club lofts of 10 degrees, 20degrees, 30 degrees, and 40 degrees, respectively. Using standardstatistical methods, such as linear regression methods, a linearrelationship (i.e., a line equation) that best fits data points 151-154may be determined. Once such a linear relationship has been determined,slope 201 may be the slope of the corresponding line equation.

Any number of such data points may be included in a best-fit linedetermination. As depicted in FIG. 27, eight data points 151-158corresponding with ball back-spin measurements have been obtained usingeight golf clubs having club lofts from 10 degrees through 45 degrees,in 5-degree increments. A linear relationship that best fits data points151-158 may be determined, and once such a linear relationship has beendetermined, slope 201 may be the slope of the corresponding lineequation.

In addition to characterizing golf ball performance on the basis of alinear spin slope, golf ball performance may also be characterized onthe basis of spin as a general function of club loft. In suchalternative characterizations, spin as a function of club loft may berepresented as a non-straight-line function in x/y coordinate system100. Some non-straight-line spin functions may be considered to have aplurality of ranges of club loft, and within each range of club loft themeasured ball spin may have separate linear relationships, such asseparate best-fit lines having different corresponding line equations.

Club lofts may also change among different sets of golf clubs. Forexample, a particular numerically-designated golf club (i.e., a 9-iron)in one set of golf clubs may have a different club loft than a golf clubof the same numerical designation (i.e., another 9-iron) in a differentset of golf clubs. Accordingly, spin slope determinations may madeseparately made using two different sets of golf clubs correspondingwith two different sets of club lofts, and thereafter compared with eachother, despite the difference in club loft among the various golf clubsof the two different sets.

Determinations of spin slope as described above may be used in methodsfor providing a selection of a recommended golf ball. In such methods,first spin slope 201 may be calculated with respect to first golf ball1100, second spin slope 202 may be calculated with respect to secondgolf ball 1200, and the recommended golf ball may be either first golfball 1100 or second golf ball 1200 based upon first spin slope 201 andsecond spin slope 202. For example, the recommended golf ball may befirst golf ball 1100 if first spin slope 201 is greater than second spinslope 202, while the recommended golf ball may be second golf ball 1200if second spin slope 202 is greater than first spin slope 201.

In calculating various spin slopes, with reference to FIGS. 20-24, datapoints 151-154 may be obtained by directly measuring ball back-spin uponstriking golf balls 1100 and 1200 with various golf clubs. However, datapoints 151-154 may be otherwise obtained. For example, data points151-154 may be measured beforehand, and may serve as numerical inputs tomethods for providing a selection of a recommended golf ball.

As discussed above, data points 151-154 may be obtained undersubstantially similar conditions. For example, both the set of datapoints 151 and 152 as well as the set of data points 153 and 154 may becollected through mechanical, machine-based, or otherwise automatedstriking of golf balls. In alternate methods, one set of data points maybe obtained from a player striking a reference golf ball, and the otherset may be a reference set of measurements corresponding with thereference golf ball. The reference golf ball may be a preselected golfball used in collecting data points, or it may be a golf ball ofpredetermined construction, such as a USGA calibration or control ball.

For example, data points 151 and 152 may be a reference set ofmeasurements corresponding with a reference golf ball, while data points153 and 154 may be obtained from a player striking the reference golfball, for purposes of custom-fitting a particular player to a particulargolf ball on the basis of spin slope. In such methods, when first spinslope 201 is greater than second spin slope 202, the recommended golfball may be a first golf ball, whereas when second spin slope 202 isgreater than first spin slope 201, the recommended golf ball may be asecond golf ball different from the first golf ball. The selection ofthe recommended golf ball may in turn reflect the better suitability ofthe first golf ball or the second golf ball for the player, on the basisof the relationship between the reference spin slope and the spin slopedetermined from measurements of the player's strikes.

Alternatively, some players may prefer golf balls having lesser spinslopes. Such preferences may relate to factors such as a player'sexperience level and a player's preferred ball performancecharacteristics. In custom-fitting such players to particular golf ballson the basis of spin slope, when first spin slope 201 is less thansecond spin slope 202, the recommended golf ball may be the first golfball, whereas when second spin slope 202 is less than first spin slope201, the recommended golf ball may be the second golf ball.

In addition to being used in methods for providing a selection of arecommended golf ball, determinations of spin slope may be used inmethods for providing a selection of a recommended golf ballconstruction between a plurality of golf ball constructions. Forexample, a first golf ball may have a first ball construction and asecond golf ball may have a second, different ball construction. A setof spin measurements may be obtained for each golf ball based upon whicha spin slope may be determined for each golf ball. Then, if the spinslope corresponding with the first golf ball is greater than the spinslope corresponding with the second golf ball, the recommended golf ballconstruction may be the first ball construction; or, if the spin slopecorresponding with the second golf ball is greater than the spin slopecorresponding with the first golf ball, the recommended golf ballconstruction may be the second ball construction.

Moreover, determinations of spin slope may be used in methods forproviding a selection of a recommended configuration of one or moreparticular ball construction components. For example, a first golf ballmay have a first configuration of a particular ball constructioncomponent, and a second golf ball may have a second, differentconfiguration of the same ball construction component. A set of spinmeasurements may be obtained for each golf ball based upon which a spinslope may be determined for each golf ball. Then, if the spin slopecorresponding with the first golf ball is greater than the spin slopecorresponding with the second golf ball, the recommended configurationof the particular ball construction component may be the firstconfiguration of the ball construction component; or, if the spin slopecorresponding with the second golf ball is greater than the spin slopecorresponding with the first golf ball, the recommended configuration ofthe particular ball construction component may be the secondconfiguration of the ball construction component.

In some methods, alternate spin slope criteria may be used in forproviding a selection between a plurality of golf balls, golf ballconstructions, or configurations of ball construction components. Asdiscussed above, a recommended golf ball may be a first golf ball whenthe first golf ball (or a golf ball construction of the first golf ball,or a configuration of a ball construction component corresponding withthe first golf ball) results in a greater or larger spin slope than thespin slope of a second golf ball. In contrast, under an alternate spinslope criteria, a recommended golf ball may be a first golf ball whenthe first golf ball (or a golf ball construction of the first golf ball,or a configuration of a ball construction component corresponding withthe first golf ball) results in a lesser or smaller spin slope than thespin slope of a second golf ball. In general, slope is a measurement ofthe amount or degree of “steepness” of a line relative to the horizontalaxis. Accordingly, when comparing the relative measures of spin slopedescribed herein, the greater or larger slope is the slope that exhibitsa greater or larger degree of steepness relative to the horizontal.Similarly, the lesser or smaller slope is the slope that exhibits alesser or smaller degree of steepness relative to the horizontal.

Additionally, methods of providing a selection of a recommended golfball construction may also include a step of manufacturing a golf ballin accordance with the recommended golf ball construction. Similarly,methods of providing a selection of a recommended configuration of agolf ball construction component may also include a step ofmanufacturing a golf ball in accordance with the recommendedconfiguration of the golf ball construction component.

The methods discussed above may also be used to obtain measurements ofgolf shot parameters other than ball spin, and may be used to determineslopes with respect to those other golf shot parameters. For example,some methods may obtain measurements related to parameters such asflight distance, carry distance, or total distance. Such methods maythen determine a distance slope with respect to that parameter by (a)obtaining sets of distance measurements, each set containingmeasurements corresponding with a plurality of golf clubs, then (b)determining a distance slope for each set of distance measurements. Thedistance slopes would in turn be the ratio of a difference betweendistance measurements to a difference between club loft among two ormore points within each set.

In addition, the methods discussed above may be used to evaluateperformance characteristics of various golf clubs, such as spin slopecharacteristics for various golf clubs. By way of example, the methodsdescribed above may be used to obtain measurements of golf shotparameters, such as ball back-spin, for a plurality of golf clubs to becompared with each other, using a reference golf ball. The ballback-spin measurements obtained for each of the plurality of golf clubsmay then be used to determine separate spin slopes for each club andprovide a selection of a recommended golf club between the plurality ofgolf clubs upon based upon a comparison of the spin slopes.

The use of calibration balls may be incorporated into the methodsdiscussed above. A calibration ball, or control ball, may be a ballsatisfying specifications established by the USGA (United States GolfAssociation) in a particular year. Calibration balls may be used tocompare the characteristics of a plurality of golf clubs, or of aplurality of golf swing sources, including golf swings taken by golfersand golf swings taken by machines. The characteristics being comparedmay therefore include various swing parameters, launch conditionparameters, and other golf shot parameters.

For example, a calibration ball may be used in the course of obtaining aset of ball back-spin measurements for a plurality of golf clubs undercontrolled testing conditions, for example tests performed underlaboratory conditions or using an indoor test range. The ball back-spinmeasurements may be obtained with care being taken to ensure thatvarious testing conditions are substantially the same, and are withinstandard engineering and testing tolerances. On the basis of the ballback-spin measurements, a benchmark linear relationship among themeasurements may be determined for the calibration ball.

Ball back-spin measurements may then be similarly taken for one or moreother balls under substantially the same controlled testing conditions,and benchmark linear relationships among the measurements for each ofthose balls may be determined. The slopes of the benchmark linearrelationships for the other balls may then be expressed as beingnormalized with respect to the slope of the benchmark linearrelationship for the calibration ball. For example, if the linearrelationships are straight lines, the slope for each of the other ballsmay be a number normalized with respect to the slope for the calibrationball. The slope for the calibration ball may thus serve as a baselineslope against which the spin slopes of other balls may be compared.

For example, in FIG. 20, data points 151 and 152 may correspond with acalibration ball, and data points 153 and 154 may correspond withanother ball under measurement. Accordingly, first spin slope 201 may bea benchmark linear relationship for the calibration ball, and secondspin slope 202 may be a linear relationship for the other ball. Firstspin slope 201 may serve as a baseline slope having a value of 1. Secondspin slope 202, which is substantially similar to first spin slope 201,may have substantially the same value as the baseline slope, i.e., avalue of 1. Similarly, in FIG. 21, first spin slope 201 may serve as abaseline slope having a value of 1, and second spin slope 202 may alsohave substantially the same value.

In contrast, as depicted respectively in FIGS. 22, 23, and 24, a ballback-spin value for data point 151 may be greater than a ball back-spinvalue for data point 153 (when struck by, for example, a driver), or aball back-spin value for data point 152 may be less than a ballback-spin value for data point 154 (when struck by a wedge, forexample), or both. Accordingly, first spin slope 201 may serve as abaseline slope having a value of 1, and second spin slope 202 may have avalue greater than 1, as normalized with respect to first spin slope201.

Having obtained a baseline slope for the benchmark linear relationshipfor the calibration ball, as well as benchmark linear relationships forother balls, another set of ball back-spin measurements may be obtainedon the basis of golf swings taken by a particular golfer outside ofcontrolled testing conditions using the calibration ball, and agolfer-based linear relationship among the measurements may bedetermined for the calibration ball. The golfer-based linearrelationship may also be expressed as a number normalized with respectto the baseline slope of the benchmark linear relationship for thecalibration ball.

The baseline slope of the benchmark linear relationship may then becompared with the slope of the golfer-based linear relationship. On thebasis of that comparison, and taking into account other golf shotparameters that may characterize golf shots taken by the golfer—forexample, distance—as well as other factors including cost, one of thenon-calibration balls may be recommended to complement or to maximizeone or more parameters associated with the golfer's golf shots.

Methods such as those discussed above may also be executed bycomputer-based ball fitting systems, such as the systems disclosed incommonly owned U.S. Pat. No. 8,758,169, entitled “Method and System forGolf Ball Fitting Analysis,” filed on Jul. 7, 2009, which is hereinincorporated by reference, and the systems disclosed in copending andcommonly owned U.S. Pat. Application Publication No. 20130190904,entitled “Method And System For Developing A Golf Ball Construction,”filed on Jul. 26, 2012, which is herein incorporated by reference.

Such systems may include a computer, which may include, but is notlimited to: a desktop computer, portable computer, tablet computer,smartphone, and/or any other device including a processor and/or adisplay that is configured to allow a user to view and/or interact withinformation. The computer may, in turn, include a CPU, a memory, adisplay, and a data transfer connection.

Computer-based ball fitting systems may include one or more automatedmeasurement devices for obtaining measurements related to golf shotparameter values as well as a device for determining spin slopes andother relationships between golf shot parameter measurements. Suchsystems may also include a device to compare the spin slopes and linearrelationships, and may include an output device, for example a printeror display, for providing a selection of a recommended golf ball betweena plurality of golf balls on the basis of such comparisons. Whenexecuting methods such as those discussed above, these systems may (1)obtain measurements using the automated measurement devices, (2) use thedetermining device to determine spin slopes, (3) use the comparingdevice to compare the spin slopes, and (4) use the output device toprovide a selection of a recommended golf ball between the golf balls.

While various embodiments of the invention have been described, thedescription is intended to be exemplary rather than limiting, and itwill be apparent to those of ordinary skill in the art that many moreembodiments and implementations are possible that are within the scopeof the invention. Accordingly, the invention is not to be restrictedexcept in light of the attached claims and their equivalents. Also,various modifications and changes may be made within the scope of theattached claims.

What is claimed is:
 1. A method for providing a selection of arecommended golf ball, the method comprising steps of: (i) obtaining (a)a first set of measurements for a first golf ball, including at leastone ball spin measurement for each of a plurality of golf clubs havingdifferent club lofts, and (b) a second set of measurements for a secondgolf ball, including at least one ball spin measurement for each of theplurality of golf clubs; (ii) determining (a) a first spin slope basedupon the first set of measurements, and (b) a second spin slope basedupon the second set of measurements; and (iii) providing a selection ofa recommended golf ball between the first golf ball and the second golfball; wherein the recommended golf ball is the first golf ball if thefirst spin slope is larger than the second spin slope, and therecommended golf ball is the second golf ball if the first spin slope isnot larger than the second spin slope.
 2. The method of claim 1, whereinthe first set of measurements is obtained by measuring strikes of thefirst golf ball, and the second set of measurements is obtained bymeasuring strikes of the second golf ball.
 3. The method of claim 1,wherein a first club loft of the plurality of club lofts correspondswith a driver, and a second club loft of the plurality of club loftscorresponds with a wedge.
 4. The method of claim 1, wherein one of thefirst set of measurements and the second set of measurements includes acomposite measurement.
 5. The method of claim 1, wherein one of thefirst spin slope and the second spin slope is based at least in partupon normalized differences between measurements.
 6. The method of claim1, wherein one of the first spin slope and the second spin slope isbased at least in part upon normalized measurements.
 7. The method ofclaim 1, wherein the first spin slope is based upon a line best fittingthe first set of measurements and the second spin slope is based upon aline best fitting the second set of measurements.
 8. The method of claim1, wherein the first golf ball has a first configuration of a ballconstruction component, the second golf ball has a second configurationof the ball construction component, and the first configuration isdifferent from the second configuration.
 9. The method of claim 8,wherein the ball construction component is one of a number of pieces orlayers, a golf ball cover material, a golf ball cover material hardness,a number of dimples in a golf ball cover, and a thickness of the golfball cover.
 10. A method for providing a selection of a recommended golfball, the method comprising steps of: (i) obtaining (a) a first set ofball spin measurements from a player making strikes with a firstplurality of striking objects having different lofts, and (b) a secondset of ball spin measurements from reference strikes made with a secondplurality of striking objects having different lofts; (ii) determining(a) a first linear relationship among the first set of ball spinmeasurements, and (b) a second linear relationship among the second setof ball spin measurements; and (iii) providing a selection of arecommended golf ball between a first golf ball and a second golf ballon the basis of at least the first linear relationship, the secondlinear relationship, and a spin slope criteria, wherein theconfiguration of a ball construction component of the second golf ballis different from the configuration of the ball construction componentof the first golf ball.
 11. The method of claim 10, wherein one of thefirst set (measurements and the second set of measurements includes acomposite measurement.
 12. The method of claim 10, wherein the secondset of measurements is obtained through measurements of golf ball spinupon machine-based strikes.
 13. The method of claim 10, wherein thesecond set of measurements is measured beforehand.
 14. The method ofclaim 10, wherein one of the first plurality of striking objects and thesecond plurality of striking objects includes a plurality of golf clubs.15. The method of claim 10, wherein a first striking object of the firstplurality of striking objects is a driver, and a second striking objectof the first plurality of striking objects is a wedge.
 16. The method ofclaim 10, wherein the ball construction component is one of a number ofpieces or layers, a golf ball cover material, a golf ball cover materialhardness, a number of dimples in a golf ball cover, and a thickness ofthe golf ball cover.
 17. The method of claim 10, wherein one of thefirst linear relationship and the second linear relationship is based atleast in part upon normalized differences between measurements.
 18. Themethod of claim 10, wherein one of the first linear relationship and thesecond linear relationship is based at least in part upon normalizedmeasurements.
 19. The method of claim 10, wherein the first linearrelationship is based upon a line best fitting the first set ofmeasurements.
 20. The method of claim 10, wherein the spin slopecriteria is which of the first linear relationship and the second linearrelationship is the larger linear relationship, and wherein therecommended golf ball is the first golf ball if the first linearrelationship is the larger linear relationship.
 21. A method forproviding a selection of a recommended golf ball, the method comprisingsteps of: (i) obtaining (a) a first set of measurements for a first golfball, including at least one ball spin measurement for each of aplurality of golf clubs that each having a different club loft, and (b)a second set of measurements for a second golf ball, including at leastone ball spin measurement for each of the plurality of golf clubs; (ii)determining (a) a first spin slope based upon the first set ofmeasurements, and (b) a second spin slope based upon the second set ofmeasurements; and (iii) providing a selection of a recommended golf ballbetween the first golf ball and the second golf ball; wherein therecommended golf ball is selected based on a difference between thefirst spin slope and the second spin slope.